Abstract
This paper presents a superconvergence analysis for the Shortley–Weller finite difference approximation of Poisson's equation with unbounded derivatives on a polygonal domain. In this analysis, we first formulate the method as a special finite element/volume method. We then analyze the convergence of the method in a finite element framework. An O ( h 1.5 ) -order superconvergence is derived for the solution derivatives in a discrete H 1 norm.
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